Question

Consider a parallel plate capacitor with plates 20 cm by 20 cm and separated by 2 mm. The dielectric constant of the material between the plates is 5.The plates are connected to a voltage source of 500 V. The energy density of the field between the plates will be close to

• A. 2.65 J/$m^3$
• B. 1.95 J/$m^3$
• C. 1.38 J/$m^3$
• D. 0.69 J/$m^3$

Answer 1

The correct option is C 1.38 J/$m^3$

Electric field density or energy per unit volume is $u=\frac{K{\epsilon }_0}{2}{\left(\frac{V}{d}\right)}^2$
$K=5,V=500volts,d=2\times {10}^{-3}m$
$\therefore u=\frac{5}{2}\times \frac{1}{4\pi \times 9\times {10}^9}\times \frac{{\left(500\right)}^2}{{(2\times {10}^{-3})}^2}=1.38J{m}^{-3}$